Polygon to Triangle
Geometry
Level
2
Is it possible to draw a triangle with equal area to a given convex polygon (regular or irregular)?
No, Never
Yes, Always
Yes, Sometimes
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1 solution
I'm assuming that "draw a triangle" means to use a compass and straightedge only. The answer is yes. Let's say 4 consecutive vertices of an arbitrary convex polygon is A, B, C, D. First, draw line AD. Then draw a line parallel to AC but passing through B. Then draw line CD and extend it until it intersects the extended line AC, and call the new point P. Draw PA, which becomes the new side of the polygon, along with new side PD. The area is unchanged. Repeat until there is only a 3-sided triangle.